This section is intended to introduce various aspects of the art, which may be associated with exemplary embodiments of the present disclosure. This discussion is believed to assist in providing a framework to facilitate a better understanding of particular aspects of the present invention. Accordingly, it should be understood that this section should be read in this light, and not necessarily as admissions of prior art.
In exploration or production stages for resources, such as hydrocarbons, different types of subsurface models may be used to represent the subsurface structure, a description of a subsurface structure and material properties for a subsurface region. For example, the subsurface model may be a geologic model or a reservoir model. The geologic model may represent measured or interpreted data for the subsurface region, such as seismic data and well log data. The geologic model may be within a physical space or domain, and may include objects (e.g., horizons, faults, volumes, and the like) and may have material properties associated with the various objects. The geologic model may also be discretized with a mesh or a grid that includes nodes and forms cells (e.g., blocks or elements) within the model. The reservoir model may be generated from the geologic model and may be used to simulate flow of fluids within the subsurface region. Accordingly, the reservoir model may use the same grid and/or cells, or may upscale the grid and/or cells to lessen the computations for simulating the fluid flow.
The development of the geologic model may be problematic. For example, populating n-dimensional (nD) spaces or domains with material properties where the space includes multiple separate nD objects is a problematic process in forming the subsurface models. The objects may partially contact each other, thus, forming a non-manifold topology. Further, the material properties in the space are typically assigned, which may be performed by a designer, modeler or user, to only one continuous object at a time. For flexibility in this approach, the original or physical domain, which may be referred to as a “physical space”, may be mapped to a design domain, which may be referred to as a “design space”. The design space includes the separate objects, which are pieced together based on some geometric criterion, and may form a continuous volume or an unfaulted volume. The mapping should be performed in manner to minimize deformation and to preserve in the design space the resemblance to the physical space (e.g., the original domain). This mapping is then used to facilitate the populating of the design space with the material properties.
For example, in geologic modeling of a subsurface region, a three-dimensional (3D) model domain is delineated by horizons and faults, where horizons are primarily flat horizontal surfaces related to deposition of sediment material forming a reservoir rock, and faults are discontinuities in the rock introduced by non-depositional events. The material properties, such as the rock properties, are typically described in a continuous volume in the design space or depositional space, which may be provided by the user or modeler, while the physical space of the subsurface model may be a discontinuous volume that includes discontinuities in the form of post-depositional faults. Construction of design space corresponds to generation of a continuous volume from a faulted structural framework by removing the discontinuities, such as nodal slips.
As another example, U.S. Pat. No. 7,480,205 describes a method of solving geo-mechanical equations for a displacement field using a mesh that conforms to the horizons and faults in a geological model. This method involves the user specifying a slip vector and may involve time consuming iterations to resolve penetrations and gaps between fault blocks. As such, this method may be problematic because specifying the slip vector may be challenging and the interiors points may not match.
As yet another example, U.S. Pat. No. 8,315,845 describes a method of solving geomechanical equations for a displacement field using a mesh that conforms to the horizons and faults in the framework. While this method does not require the user to specify a slip vector, the method involves representing more than one horizon to be substantially planer and parallel. Further, the method does not measure, much less, reduce penetration or gaps between fault blocks away from fault/horizon intersections. Additionally, the requirement to flatten by specifying boundary conditions for more than one horizon may significantly distort the layer thickness profile in the physical space.
In U.S. Pat. No. 7,711,532, the method describes “parametric” mapping to the design space, which is defined by solving a constrained optimization problem for three transfer functions u,v,t on supporting 3D tetrahedral meshes that conforms to fault surfaces. The method describes that only tetrahedral mesh may be used, some of the constraints are heuristic and may be application-dependent, and special handling is required for erosional horizons.
Other conventional approaches, such as U.S. Pat. No. 6,106,561, are based on utilizing the ijk indexing system of the corner point grid built in the physical space for mapping to design space. Thus, generation of the mapping logic is combined with the logic for corner-point grid generation. Such kinds of mappings are very approximate and do not account for volume distortion of corner-point cells.
Accordingly, there remains a need in the industry for methods and systems that are more efficient and may be constructed to lessen problems associated with discontinuities in geologic modeling. The present techniques provide a method and apparatus that overcome one or more of the deficiencies discussed above.